When 3x⁴ + 2x³ − x² + 5 is divided by (x² + 1), the remainder is:

Question

Accepted Answer

−2x + 9. Long division: 3x²(x² + 1) = 3x⁴ + 3x² leaves 2x³ − 4x² + 5; then 2x(x² + 1) = 2x³ + 2x leaves −4x² − 2x + 5; then −4(x² + 1) = −4x² − 4 leaves −2x + 9, whose degree is below 2 so the division stops. (Forgetting the −4 that comes with the last step leaves −2x + 5.) Check: (x² + 1)(3x² + 2x − 4) + (−2x + 9) = 3x⁴ + 2x³ − x² + 5.

When $3 x^{4} + 2 x^{3} - x^{2} + 5$ is divided by $(x^{2} + 1)$ , the remainder is:

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When 3x4+2x3−x2+5 is divided by (x2+1), the remainder is:

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Master this topic in 30 minutes a day.

More Algebra practice

When $3 x^{4} + 2 x^{3} - x^{2} + 5$ is divided by $(x^{2} + 1)$ , the remainder is: